On Approximate Balanced Bi-clustering

In this paper, we consider the so-called balanced bi-clustering problem for n entities in a suitable space where the number of entities in each cluster is bounded. A special case of the balanced bi-clustering, where the number of entities in each cluster is fixed, is discussed. We present several algorithms, including deterministic and heuristic to attack these problems. In particular, a novel and efficient heuristic, in which we first reformulate the constrained bi-clustering problem into a quadratic programming(QP) problem and then try to solve it by optimization technique, is proposed. We prove that our approximation algorithm can provide a 2-approximate solution to the original problem. Promising numerical results are reported.